Mozannar et al. (2020)
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This appears to be a fluid dynamics paper on viscoelastic flows through porous media, unrelated to AI safety. Likely misclassified or requires verification of actual content relevance to AI safety research.
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Abstract
Viscoelastic flows through microscale porous arrays exhibit complex path-selection and switching phenomena. However, understanding this process is limited by a lack of studies linking between a single object and large arrays. Here, we report experiments on viscoelastic flow past side-by-side microcylinders with variable intercylinder gap. With increasing flow rate, a sequence of two imperfect symmetry-breaking bifurcations forces selection of either one or two of the three possible flow paths around the cylinders. Tuning the gap length through the value where the first bifurcation becomes perfect reveals regions of bi and tristability in a dimensionless flow rate-gap length `phase' diagram.
Summary
This experimental study investigates viscoelastic flow behavior around side-by-side microcylinders with variable spacing. The research demonstrates that increasing flow rates trigger symmetry-breaking bifurcations that force the fluid to select specific flow paths around the cylinders. By systematically varying the gap between cylinders, the authors map regions of bistability and tristability in a phase diagram, providing insights into path-selection mechanisms in viscoelastic flows through microscale porous structures.
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[2010.14749] Tristability in viscoelastic flow past side-by-side microcylinders
Tristability in viscoelastic flow past side-by-side microcylinders
Cameron C. Hopkins
Simon J. Haward
Amy Q. Shen
Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa, 904-0495, Japan
Abstract
Viscoelastic flows through microscale porous arrays exhibit complex path-selection and switching phenomena. However, understanding this process is limited by a lack of studies linking between a single object and large arrays. Here, we report experiments on viscoelastic flow past side-by-side microcylinders with variable intercylinder gap. With increasing flow rate, a sequence of two imperfect symmetry-breaking bifurcations forces selection of either one or two of the three possible flow paths around the cylinders. Tuning the gap length through the value where the first bifurcation becomes perfect reveals regions of bi and tristability in a dimensionless flow rate-gap length ‘phase’ diagram.
† † preprint: APS/123-QED
Since the advent of microfluidics in the early 2000s [ 1 , 2 ] , geometries with length-scales ℓ ∼ O ( 100 μ \ell\sim O(100~{}\mu m) have become a vital tool in experimental fluid dynamics. At the microscale, viscoelastic fluids (with properties between viscous liquids and elastic solids) can flow with negligible inertia (Reynolds number Re ∼ ℓ ≪ 1 similar-to Re ℓ much-less-than 1 \textnormal{Re}\sim\ell\ll 1 ), but high elasticity (Weissenberg number Wi ∼ ℓ − 1 ≫ 1 similar-to Wi superscript ℓ 1 much-greater-than 1 \textnormal{Wi}\sim\ell^{-1}\gg 1 ) [ 2 ] . In such flows, elasticity becomes the dominant source of nonlinearity, leading to instabilities [ 3 , 4 , 5 , 6 , 7 , 8 , 9 ] , and time-dependency that impact widespread processes ranging from jet fragmentation [ 10 , 11 ] to hemodynamics [ 12 , 13 ] and porous media flows [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ] . In particular, the path selection and switching phenomena in viscoelastic porous media flow is considered of fundamental importance in processes such as enhanced oil recovery, groundwater remediation, filtration, and drug delivery [ 14 , 15 , 16 , 17 , 18 , 19 ] .
Porous media are frequently modeled by ordered and disordered arrays of microfluidic circular cylinders [ 15 , 16 , 17 , 18 , 19 ] . Flow past a single circular cylinder in a channel is an archetypal problem in fluid dynamics, and a ‘benchmark’ for studying viscoelastic flows. The stagnation point downstream of a cylinder is a location where streamline curvature combines with strong velocity gradients; conditions that render viscoelastic base flows prone to instability and downstream fluctuations [ 21 , 22 , 23 , 24 ] . For fluids with a shear-rate-dependent viscosity (i.e., shear-thinning), the perturbation to the base flow can lead to a steady symmetry-breaking flow bifurcation where the viscoelastic fluid selec
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